The advantage the 911 Turbo S has going for it in addition to the weight advantage is a dual clutch transmission. The E63 AMG S is using an MCT automatic. Stock for stock, the 911 Turbo S is the quicker and faster car.
However, this E63 AMG S is not stock and features tuning courtesy of GAD Motors. What exactly is done is not stated but it looks to be much more than just a tune based on the result. The 991 Turbo S gets pulled and pulled hard by 170 miles per hour. This E63 is just making much more power than what likely is a stock 991 Turbo S.